11:45 AM - 12:00 PM
[AAS09-05] Spatial interpolation method for estimation of charge distribution in thunderstorm
Keywords:Geostatistics, Kriging, Charge distribution estimation, Thunderstorm
Accurate interpolation is essential for improving estimation of charge distribution in a thunderstorm[Mansell et al., 2005]. Ordinary Kriging[Cressie, 1988] is widely used due to its ability to incorporate spatial correlations, result in high-accuracy interpolations when observation data are dense and well-distributed.
However, its performance heavily depends on the density of the observed data, leading to significant error when data points are sparse. To address this issue, we propose a novel interpolation method based on Ordinary Kriging. Our approach is to see the observed variable as the sum of two random variables: a physical model term and an observation error term. By assuming their probability distribution, we can analytically derive the error variance function to minimize and determine optimal interpolation weights.
To evaluate the effectiveness, we calculated the performance of proposed method to apply interpolation of electric field on one-dimensional space whose observation data was given by simulation by two ways, confirming the superiority of the proposed method when data points are sparse:(1) Comparison of root mean square error between Ordinary Kriging and the proposed method and (2) Estimation of charge distribution in a given domain using observed and interpolated electric field data to quantify the resolution improvement.
Finally, we applied the proposed method to actual observed electric field data and estimate charge distribution in a real thunderstorm. The results demonstrated that our approach enables higher resolution for estimation, even when observation point are limited to only six with in an approximately 10 square kilometers area. The proposed method shows significant advantages in cases with limited observation data, where Ordinary Kriging struggles due to high dependency on variogram fitting.
However, its performance heavily depends on the density of the observed data, leading to significant error when data points are sparse. To address this issue, we propose a novel interpolation method based on Ordinary Kriging. Our approach is to see the observed variable as the sum of two random variables: a physical model term and an observation error term. By assuming their probability distribution, we can analytically derive the error variance function to minimize and determine optimal interpolation weights.
To evaluate the effectiveness, we calculated the performance of proposed method to apply interpolation of electric field on one-dimensional space whose observation data was given by simulation by two ways, confirming the superiority of the proposed method when data points are sparse:(1) Comparison of root mean square error between Ordinary Kriging and the proposed method and (2) Estimation of charge distribution in a given domain using observed and interpolated electric field data to quantify the resolution improvement.
Finally, we applied the proposed method to actual observed electric field data and estimate charge distribution in a real thunderstorm. The results demonstrated that our approach enables higher resolution for estimation, even when observation point are limited to only six with in an approximately 10 square kilometers area. The proposed method shows significant advantages in cases with limited observation data, where Ordinary Kriging struggles due to high dependency on variogram fitting.